As disclosed in German Offenlegungsschrift No. 3,600,943, it has previously been customary to optimize and keep constant the discharge pressure and the discharge current intensity matched to the element to be detected, during the atomization and excitation steps of the analytical cycle. This method is permissible for the simultaneous analysis of several elements if the atomization of the analyte components are to start or proceed to completion at approximately the same temperature. Such elements are, for example, Mn, Cr, Fe, Co. A different group is formed by Cd, Zn, Pb, Au, Ag. If analytes containing elements from both groups or even other elements are to be analyzed, a satisfactory analytical result for all the elements to be detected cannot be obtained by keeping the parameters of discharge pressure and discharge current intensity constant within the same analytical cycle.